{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "view-in-github"
      },
      "source": [
        "\u003ca href=\"https://colab.research.google.com/github/tensorflow/tpu/blob/master/tools/colab/mnist_tpuestimator.ipynb\" target=\"_parent\"\u003e\u003cimg src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/\u003e\u003c/a\u003e"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "N6ZDpd9XzFeN"
      },
      "source": [
        "##### Copyright 2018 The TensorFlow Hub Authors.\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "cellView": "form",
        "colab": {},
        "colab_type": "code",
        "id": "KUu4vOt5zI9d"
      },
      "outputs": [],
      "source": [
        "# Copyright 2018 The TensorFlow Hub Authors. All Rights Reserved.\n",
        "#\n",
        "# Licensed under the Apache License, Version 2.0 (the \"License\");\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "#     http://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License.\n",
        "# =============================================================================="
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "xqLjB2cy5S7m"
      },
      "source": [
        "## MNIST Estimator to TPUEstimator\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "39I6y3QJsb6t"
      },
      "source": [
        "## Overview\n",
        "\n",
        "This notebook  will show you how to port an Estimator model to TPUEstimator.\n",
        "\n",
        "All the lines that had to be changed in the porting are marked with a \"TPU REFACTORING\" comment.\n",
        "\n",
        "You do the porting only once. TPUEstimator then works on both TPU and GPU with the `use_tpu=False` flag.\n",
        "\n",
        "This notebook is hosted on GitHub. To view it in its original repository, after opening the notebook, select **File \u003e View on GitHub**."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "j_k5L8WB9KWa"
      },
      "source": [
        "Note: This notebook starts with the code included in the [MNIST Estimator](https://colab.research.google.com/github/tensorflow/tpu/blob/master/tools/colab/mnist_estimator.ipynb) notebook. This conversion enables your model to take advantage of Cloud TPU to speed up training computations."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "avJXF3ofBAmg"
      },
      "source": [
        "## Learning objectives\n",
        "\n",
        "In this notebook, you will learn how to port an Estimator model to TPUEstimator."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "SOMDaCK97FIq"
      },
      "source": [
        "## Instructions"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "_I0RdnOSkNmi"
      },
      "source": [
        "\u003ch3\u003e\u003ca href=\"https://cloud.google.com/tpu/\"\u003e\u003cimg valign=\"middle\" src=\"https://raw.githubusercontent.com/GoogleCloudPlatform/tensorflow-without-a-phd/master/tensorflow-rl-pong/images/tpu-hexagon.png\" width=\"50\"\u003e\u003c/a\u003e  \u0026nbsp;\u0026nbsp;Train on TPU\u003c/h3\u003e\n",
        "\n",
        "   1. Create a Cloud Storage bucket for your TensorBoard logs at http://console.cloud.google.com/storage and fill in the BUCKET parameter in the \"Parameters\" section below.\n",
        " \n",
        "   1. On the main menu, click Runtime and select **Change runtime type**. Set \"TPU\" as the hardware accelerator.\n",
        "   1. Click Runtime again and select **Runtime \u003e Run All** (Watch out: the \"Colab-only auth for this notebook and the TPU\" cell requires user input). You can also run the cells manually with Shift-ENTER.\n",
        "\n",
        "\u003ch3\u003e\u003ca href=\"https://cloud.google.com/ml-engine/\"\u003e\u003cimg valign=\"middle\" src=\"https://raw.githubusercontent.com/GoogleCloudPlatform/tensorflow-without-a-phd/master/tensorflow-rl-pong/images/mlengine-hexagon.png\" width=\"50\"\u003e\u003c/a\u003e  \u0026nbsp;\u0026nbsp;Deploy to Cloud Machine Learning (ML) Engine\u003c/h3\u003e\n",
        "1. At the bottom of this notebook you can deploy your trained model to ML Engine for a serverless, autoscaled, REST API experience. You will need a GCP project name for this last part.\n",
        "\n",
        "TPUs are located in Google Cloud, for optimal performance, they read data directly from Google Cloud Storage (GCS)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "Lvo0t7XVIkWZ"
      },
      "source": [
        "## Data, model, and training"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "qpiJj8ym0v0-"
      },
      "source": [
        "### Imports"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "colab_type": "code",
        "id": "4Ru_7bw-xyoP",
        "outputId": "03b2474c-c1c6-4431-a264-1c01440d5f1d"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Tensorflow version 1.13.1\n"
          ]
        }
      ],
      "source": [
        "import os, re, math, json, shutil, pprint, datetime\n",
        "import PIL.Image, PIL.ImageFont, PIL.ImageDraw  # \"pip3 install Pillow\" or \"pip install Pillow\" if needed\n",
        "import numpy as np\n",
        "import tensorflow as tf\n",
        "from matplotlib import pyplot as plt\n",
        "from tensorflow.python.platform import tf_logging\n",
        "print(\"Tensorflow version \" + tf.__version__)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "aBDGQWkbLGvh"
      },
      "source": [
        "### Parameters"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "_V_VbLELLJCS"
      },
      "outputs": [],
      "source": [
        "BATCH_SIZE = 32 #@param {type:\"integer\"}\n",
        "BUCKET = 'gs://' #@param {type:\"string\"}\n",
        "\n",
        "assert re.search(r'gs://.+', BUCKET), 'You need a GCS bucket for your Tensorboard logs. Head to http://console.cloud.google.com/storage and create one.'\n",
        "\n",
        "training_images_file   = 'gs://mnist-public/train-images-idx3-ubyte'\n",
        "training_labels_file   = 'gs://mnist-public/train-labels-idx1-ubyte'\n",
        "validation_images_file = 'gs://mnist-public/t10k-images-idx3-ubyte'\n",
        "validation_labels_file = 'gs://mnist-public/t10k-labels-idx1-ubyte'"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "cellView": "form",
        "colab": {},
        "colab_type": "code",
        "id": "qhdz68Xm3Z4Z"
      },
      "outputs": [],
      "source": [
        "#@title visualization utilities [RUN ME]\n",
        "\"\"\"\n",
        "This cell contains helper functions used for visualization\n",
        "and downloads only. You can skip reading it. There is very\n",
        "little useful Keras/Tensorflow code here.\n",
        "\"\"\"\n",
        "\n",
        "# Matplotlib config\n",
        "plt.rc('image', cmap='gray_r')\n",
        "plt.rc('grid', linewidth=0)\n",
        "plt.rc('xtick', top=False, bottom=False, labelsize='large')\n",
        "plt.rc('ytick', left=False, right=False, labelsize='large')\n",
        "plt.rc('axes', facecolor='F8F8F8', titlesize=\"large\", edgecolor='white')\n",
        "plt.rc('text', color='a8151a')\n",
        "plt.rc('figure', facecolor='F0F0F0')# Matplotlib fonts\n",
        "MATPLOTLIB_FONT_DIR = os.path.join(os.path.dirname(plt.__file__), \"mpl-data/fonts/ttf\")\n",
        "\n",
        "# pull a batch from the datasets. This code is not very nice, it gets much better in eager mode (TODO)\n",
        "def dataset_to_numpy_util(training_dataset, validation_dataset, N):\n",
        "  \n",
        "  # get one batch from each: 10000 validation digits, N training digits\n",
        "  unbatched_train_ds = training_dataset.unbatch()\n",
        "  v_images, v_labels = validation_dataset.make_one_shot_iterator().get_next()\n",
        "  t_images, t_labels = unbatched_train_ds.batch(N).make_one_shot_iterator().get_next()\n",
        "  \n",
        "  # Run once, get one batch. Session.run returns numpy results\n",
        "  with tf.Session() as ses:\n",
        "    (validation_digits, validation_labels,\n",
        "     training_digits, training_labels) = ses.run([v_images, v_labels, t_images, t_labels])\n",
        "  \n",
        "  # these were one-hot encoded in the dataset\n",
        "  validation_labels = np.argmax(validation_labels, axis=1)\n",
        "  training_labels = np.argmax(training_labels, axis=1)\n",
        "  \n",
        "  return (training_digits, training_labels,\n",
        "          validation_digits, validation_labels)\n",
        "\n",
        "# create digits from local fonts for testing\n",
        "def create_digits_from_local_fonts(n):\n",
        "  font_labels = []\n",
        "  img = PIL.Image.new('LA', (28*n, 28), color = (0,255)) # format 'LA': black in channel 0, alpha in channel 1\n",
        "  font1 = PIL.ImageFont.truetype(os.path.join(MATPLOTLIB_FONT_DIR, 'DejaVuSansMono-Oblique.ttf'), 25)\n",
        "  font2 = PIL.ImageFont.truetype(os.path.join(MATPLOTLIB_FONT_DIR, 'STIXGeneral.ttf'), 25)\n",
        "  d = PIL.ImageDraw.Draw(img)\n",
        "  for i in range(n):\n",
        "    font_labels.append(i%10)\n",
        "    d.text((7+i*28,0 if i\u003c10 else -4), str(i%10), fill=(255,255), font=font1 if i\u003c10 else font2)\n",
        "  font_digits = np.array(img.getdata(), np.float32)[:,0] / 255.0 # black in channel 0, alpha in channel 1 (discarded)\n",
        "  font_digits = np.reshape(np.stack(np.split(np.reshape(font_digits, [28, 28*n]), n, axis=1), axis=0), [n, 28*28])\n",
        "  return font_digits, font_labels\n",
        "\n",
        "# utility to display a row of digits with their predictions\n",
        "def display_digits(digits, predictions, labels, title, n):\n",
        "  plt.figure(figsize=(13,3))\n",
        "  digits = np.reshape(digits, [n, 28, 28])\n",
        "  digits = np.swapaxes(digits, 0, 1)\n",
        "  digits = np.reshape(digits, [28, 28*n])\n",
        "  plt.yticks([])\n",
        "  plt.xticks([28*x+14 for x in range(n)], predictions)\n",
        "  for i,t in enumerate(plt.gca().xaxis.get_ticklabels()):\n",
        "    if predictions[i] != labels[i]: t.set_color('red') # bad predictions in red\n",
        "  plt.imshow(digits)\n",
        "  plt.grid(None)\n",
        "  plt.title(title)\n",
        "  \n",
        "# utility to display multiple rows of digits, sorted by unrecognized/recognized status\n",
        "def display_top_unrecognized(digits, predictions, labels, n, lines):\n",
        "  idx = np.argsort(predictions==labels) # sort order: unrecognized first\n",
        "  for i in range(lines):\n",
        "    display_digits(digits[idx][i*n:(i+1)*n], predictions[idx][i*n:(i+1)*n], labels[idx][i*n:(i+1)*n],\n",
        "                   \"{} sample validation digits out of {} with bad predictions in red and sorted first\".format(n*lines, len(digits)) if i==0 else \"\", n)\n",
        "    \n",
        "# utility to display training and validation curves\n",
        "def display_training_curves(training, validation, title, subplot):\n",
        "  if subplot%10==1: # set up the subplots on the first call\n",
        "    plt.subplots(figsize=(10,10), facecolor='#F0F0F0')\n",
        "    plt.tight_layout()\n",
        "  ax = plt.subplot(subplot)\n",
        "  ax.grid(linewidth=1, color='white')\n",
        "  ax.plot(training)\n",
        "  ax.plot(validation)\n",
        "  ax.set_title('model '+ title)\n",
        "  ax.set_ylabel(title)\n",
        "  ax.set_xlabel('epoch')\n",
        "  ax.legend(['train', 'valid.'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "Lzd6Qi464PsA"
      },
      "source": [
        "### Colab-only auth for this notebook and the TPU"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "cellView": "both",
        "colab": {},
        "colab_type": "code",
        "id": "MPx0nvyUnvgT"
      },
      "outputs": [],
      "source": [
        "IS_COLAB_BACKEND = 'COLAB_GPU' in os.environ  # this is always set on Colab, the value is 0 or 1 depending on GPU presence\n",
        "if IS_COLAB_BACKEND:\n",
        "  from google.colab import auth\n",
        "  auth.authenticate_user() # Authenticates the backend and also the TPU using your credentials so that they can access your private GCS buckets"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "bLZKp8bWZdmh"
      },
      "source": [
        "### TPU detection"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "colab_type": "code",
        "id": "qQpdD_DSZjNY",
        "outputId": "5821e7d9-c7bc-4eb0-94ed-fe43c6d38e02"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Running on TPU  ['10.65.19.2:8470']\n"
          ]
        }
      ],
      "source": [
        "#TPU REFACTORING: detect the TPU\n",
        "try: # TPU detection\n",
        "  tpu = tf.contrib.cluster_resolver.TPUClusterResolver() # Picks up a connected TPU on Google's Colab, ML Engine, Kubernetes and Deep Learning VMs accessed through the 'ctpu up' utility\n",
        "  #tpu = tf.contrib.cluster_resolver.TPUClusterResolver('MY_TPU_NAME') # If auto-detection does not work, you can pass the name of the TPU explicitly (tip: on a VM created with \"ctpu up\" the TPU has the same name as the VM)\n",
        "  print('Running on TPU ', tpu.cluster_spec().as_dict()['worker'])\n",
        "  USE_TPU = True\n",
        "except ValueError:\n",
        "  tpu = None\n",
        "  print(\"Running on GPU or CPU\")\n",
        "  USE_TPU = False"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "Lz1Zknfk4qCx"
      },
      "source": [
        "### tf.data.Dataset: parse files and prepare training and validation datasets\n",
        "Please read the [best practices for building](https://www.tensorflow.org/guide/performance/datasets) input pipelines with tf.data.Dataset."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "F7yKy0bRh6R0"
      },
      "outputs": [],
      "source": [
        "def read_label(tf_bytestring):\n",
        "    label = tf.decode_raw(tf_bytestring, tf.uint8)\n",
        "    label = tf.reshape(label, [])\n",
        "    label = tf.one_hot(label, 10)\n",
        "    return label\n",
        "  \n",
        "def read_image(tf_bytestring):\n",
        "    image = tf.decode_raw(tf_bytestring, tf.uint8)\n",
        "    image = tf.cast(image, tf.float32)/255.0\n",
        "    image = tf.reshape(image, [28*28])\n",
        "    return image\n",
        "  \n",
        "def load_dataset(image_file, label_file):\n",
        "    imagedataset = tf.data.FixedLengthRecordDataset(image_file, 28*28, header_bytes=16)\n",
        "    imagedataset = imagedataset.map(read_image, num_parallel_calls=16)\n",
        "    labelsdataset = tf.data.FixedLengthRecordDataset(label_file, 1, header_bytes=8)\n",
        "    labelsdataset = labelsdataset.map(read_label, num_parallel_calls=16)\n",
        "    dataset = tf.data.Dataset.zip((imagedataset, labelsdataset))\n",
        "    return dataset \n",
        "  \n",
        "def get_training_dataset(image_file, label_file, batch_size):\n",
        "    dataset = load_dataset(image_file, label_file)\n",
        "    dataset = dataset.cache()  # this small dataset can be entirely cached in RAM, for TPU this is important to get good performance from such a small dataset\n",
        "    dataset = dataset.shuffle(5000, reshuffle_each_iteration=True)\n",
        "    dataset = dataset.repeat() # Mandatory for TPU for now\n",
        "    dataset = dataset.batch(batch_size, drop_remainder=True) # drop_remainder is important on TPU, batch size must be fixed\n",
        "    dataset = dataset.prefetch(-1)  # prefetch next batch while training  (-1: autotune prefetch buffer size)\n",
        "    return dataset\n",
        "\n",
        "#TPU REFACTORING: training and eval batch sizes must be the same: passing  batch_size parameter here too\n",
        "# def get_validation_dataset(image_file, label_file):\n",
        "def get_validation_dataset(image_file, label_file, batch_size):\n",
        "    dataset = load_dataset(image_file, label_file)\n",
        "    dataset = dataset.cache() # this small dataset can be entirely cached in RAM, for TPU this is important to get good performance from such a small dataset\n",
        "    #TPU REFACTORING: training and eval batch sizes must be the same: passing  batch_size parameter here too\n",
        "    # dataset = dataset.batch(10000, drop_remainder=True) # 10000 items in eval dataset, all in one batch\n",
        "    dataset = dataset.batch(batch_size, drop_remainder=True)\n",
        "    dataset = dataset.repeat() # Mandatory for TPU for now\n",
        "    return dataset\n",
        "\n",
        "# instantiate the datasets\n",
        "training_dataset = get_training_dataset(training_images_file, training_labels_file, BATCH_SIZE)\n",
        "validation_dataset = get_validation_dataset(validation_images_file, validation_labels_file, 10000)\n",
        "\n",
        "# For TPU, we will need a function that returns the dataset\n",
        "\n",
        "# TPU REFACTORING: input_fn's must have a params argument though which TPUEstimator passes params['batch_size']\n",
        "# training_input_fn = lambda: get_training_dataset(training_images_file, training_labels_file, BATCH_SIZE)\n",
        "# validation_input_fn = lambda: get_validation_dataset(validation_images_file, validation_labels_file)\n",
        "training_input_fn = lambda params: get_training_dataset(training_images_file, training_labels_file, params['batch_size'])\n",
        "validation_input_fn = lambda params: get_validation_dataset(validation_images_file, validation_labels_file, params['batch_size'])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "_fXo6GuvL3EB"
      },
      "source": [
        "### Let's have a look at the data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 181
        },
        "colab_type": "code",
        "id": "9aYl2IYXiycl",
        "outputId": "5c2d818b-4ebd-49b3-9f08-24f2938892e8"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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799P+/fuJ4yojfeTl5UlW95EjR8SHZk3PgdLSUlq8eLF4jX/99deSya6JsrIy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\nYII=\n",
            "text/plain": [
              "\u003cFigure size 936x216 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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1En3Iffny5ULD472LmmbXrl0EgHr37i1quYmJiWRlZVUtJKV169YUGBio1Lkn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\n",
            "text/plain": [
              "\u003cFigure size 936x216 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "N = 24\n",
        "(training_digits, training_labels,\n",
        " validation_digits, validation_labels) = dataset_to_numpy_util(training_dataset, validation_dataset, N)\n",
        "display_digits(training_digits, training_labels, training_labels, \"training digits and their labels\", N)\n",
        "display_digits(validation_digits[:N], validation_labels[:N], validation_labels[:N], \"validation digits and their labels\", N)\n",
        "font_digits, font_labels = create_digits_from_local_fonts(N)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "KIc0oqiD40HC"
      },
      "source": [
        "### Estimator model\n",
        "If you are not sure what cross-entropy, dropout, softmax or batch-normalization mean, head here for a crash-course: [Tensorflow and deep learning without a PhD](https://github.com/GoogleCloudPlatform/tensorflow-without-a-phd/#featured-code-sample)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "M9s9yHq7jMCV"
      },
      "outputs": [],
      "source": [
        "# This model trains to 99.4% sometimes 99.5% accuracy in 10 epochs\n",
        "\n",
        "# TPU REFACTORING: model_fn must have a params argument. TPUEstimator passes batch_size and use_tpu into it\n",
        "#def model_fn(features, labels, mode):\n",
        "def model_fn(features, labels, mode, params):\n",
        "\n",
        "  is_training = (mode == tf.estimator.ModeKeys.TRAIN)\n",
        "\n",
        "  x = features\n",
        "  y = tf.reshape(x, [-1, 28, 28, 1])\n",
        "\n",
        "  y = tf.layers.Conv2D(filters=6, kernel_size=3, padding='same', use_bias=False)(y) # no bias necessary before batch norm\n",
        "  y = tf.layers.BatchNormalization(scale=False, center=True)(y, training=is_training) # no batch norm scaling necessary before \"relu\"\n",
        "  y = tf.nn.relu(y) # activation after batch norm\n",
        "\n",
        "  y = tf.layers.Conv2D(filters=12, kernel_size=6, padding='same', use_bias=False, strides=2)(y)\n",
        "  y = tf.layers.BatchNormalization(scale=False, center=True)(y, training=is_training)\n",
        "  y = tf.nn.relu(y)\n",
        "\n",
        "  y = tf.layers.Conv2D(filters=24, kernel_size=6, padding='same', use_bias=False, strides=2)(y)\n",
        "  y = tf.layers.BatchNormalization(scale=False, center=True)(y, training=is_training)\n",
        "  y = tf.nn.relu(y)\n",
        "\n",
        "  y = tf.layers.Flatten()(y)\n",
        "  y = tf.layers.Dense(200, use_bias=False)(y)\n",
        "  y = tf.layers.BatchNormalization(scale=False, center=True)(y, training=is_training)\n",
        "  y = tf.nn.relu(y)\n",
        "  y = tf.layers.Dropout(0.5)(y, training=is_training)\n",
        "  \n",
        "  logits = tf.layers.Dense(10)(y)\n",
        "  predictions = tf.nn.softmax(logits)\n",
        "  classes = tf.math.argmax(predictions, axis=-1)\n",
        "  \n",
        "  if (mode != tf.estimator.ModeKeys.PREDICT):\n",
        "    loss = tf.losses.softmax_cross_entropy(labels, logits)\n",
        "\n",
        "    step = tf.train.get_or_create_global_step()\n",
        "    # TPU REFACTORING: step is now increased once per GLOBAL_BATCH_SIZE = 8*BATCH_SIZE. Must adjust learning rate schedule accordingly\n",
        "    # lr = 0.0001 + tf.train.exponential_decay(0.01, step, 2000, 1/math.e)\n",
        "    lr = 0.0001 + tf.train.exponential_decay(0.01, step, 2000//8, 1/math.e)\n",
        "    \n",
        "    # TPU REFACTORING: custom Tensorboard summaries do not work. Only default Estimator summaries will appear in Tensorboard.\n",
        "    # tf.summary.scalar(\"learn_rate\", lr)\n",
        "    \n",
        "    optimizer = tf.train.AdamOptimizer(lr)\n",
        "    # TPU REFACTORING: wrap the optimizer in a CrossShardOptimizer: this implements the multi-core training logic\n",
        "    if params['use_tpu']:\n",
        "      optimizer = tf.contrib.tpu.CrossShardOptimizer(optimizer)\n",
        "    \n",
        "    # little wrinkle: batch norm uses running averages which need updating after each batch. create_train_op does it, optimizer.minimize does not.\n",
        "    train_op = tf.contrib.training.create_train_op(loss, optimizer)\n",
        "    #train_op = optimizer.minimize(loss, tf.train.get_or_create_global_step())\n",
        "    \n",
        "    # TPU REFACTORING: a metrics_fn is needed for TPU\n",
        "    # metrics = {'accuracy': tf.metrics.accuracy(classes, tf.math.argmax(labels, axis=-1))}\n",
        "    metric_fn = lambda classes, labels: {'accuracy': tf.metrics.accuracy(classes, tf.math.argmax(labels, axis=-1))}\n",
        "    tpu_metrics = (metric_fn, [classes, labels])  # pair of metric_fn and its list of arguments, there can be multiple pairs in a list\n",
        "                                                  # metric_fn will run on CPU, not TPU: more operations are allowed\n",
        "  else:\n",
        "    loss = train_op = metrics = tpu_metrics = None  # None of these can be computed in prediction mode because labels are not available\n",
        "  \n",
        "  # TPU REFACTORING: EstimatorSpec =\u003e TPUEstimatorSpec\n",
        "  ## return tf.estimator.EstimatorSpec(\n",
        "  return tf.contrib.tpu.TPUEstimatorSpec(\n",
        "    mode=mode,\n",
        "    predictions={\"predictions\": predictions, \"classes\": classes},  # name these fields as you like\n",
        "    loss=loss,\n",
        "    train_op=train_op,\n",
        "    # TPU REFACTORING: a metrics_fn is needed for TPU, passed into the eval_metrics field instead of eval_metrics_ops\n",
        "    # eval_metric_ops=metrics\n",
        "    eval_metrics = tpu_metrics\n",
        "  )"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "DeIxkrv9Wihg"
      },
      "outputs": [],
      "source": [
        "# Called once when the model is saved. This function produces a Tensorflow\n",
        "# graph of operations that will be prepended to your model graph. When\n",
        "# your model is deployed as a REST API, the API receives data in JSON format,\n",
        "# parses it into Tensors, then sends the tensors to the input graph generated by\n",
        "# this function. The graph can transform the data so it can be sent into your\n",
        "# model input_fn. You can do anything you want here as long as you do it with\n",
        "# tf.* functions that produce a graph of operations.\n",
        "def serving_input_fn():\n",
        "    # placeholder for the data received by the API (already parsed, no JSON decoding necessary,\n",
        "    # but the JSON must contain one or multiple 'image' key(s) with 28x28 greyscale images  as content.)\n",
        "    inputs = {\"serving_input\": tf.placeholder(tf.float32, [None, 28, 28])}  # the shape of this dict should match the shape of your JSON\n",
        "    features = inputs['serving_input']  # no transformation needed\n",
        "    return tf.estimator.export.TensorServingInputReceiver(features, inputs)  # features are the features needed by your model_fn\n",
        "    # Return a ServingInputReceiver if your features are a dictionary of Tensors, TensorServingInputReceiver if they are a straight Tensor"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "RxpRgF874-ix"
      },
      "source": [
        "### Train and validate the model, this time on TPU"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 3094
        },
        "colab_type": "code",
        "executionInfo": {
          "elapsed": 46943,
          "status": "ok",
          "timestamp": 1552677762774,
          "user": {
            "displayName": "",
            "photoUrl": "",
            "userId": ""
          },
          "user_tz": 420
        },
        "id": "TTwH_P-ZJ_xx",
        "outputId": "4328d8c2-29a5-4a63-b8f4-365f8a97018d"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "WARNING:tensorflow:Estimator's model_fn (\u003cfunction model_fn at 0x7f35edda0f28\u003e) includes params argument, but params are not passed to Estimator.\n",
            "INFO:tensorflow:Using config: {'_model_dir': 'gs://gm-bucket/mnistjobs/job-2019-03-15-19:21:55', '_tf_random_seed': None, '_save_summary_steps': 100, '_save_checkpoints_steps': None, '_save_checkpoints_secs': 600, '_session_config': allow_soft_placement: true\n",
            "cluster_def {\n",
            "  job {\n",
            "    name: \"worker\"\n",
            "    tasks {\n",
            "      key: 0\n",
            "      value: \"10.18.219.10:8470\"\n",
            "    }\n",
            "  }\n",
            "}\n",
            ", '_keep_checkpoint_max': 5, '_keep_checkpoint_every_n_hours': 10000, '_log_step_count_steps': None, '_train_distribute': None, '_device_fn': None, '_protocol': None, '_eval_distribute': None, '_experimental_distribute': None, '_service': None, '_cluster_spec': \u003ctensorflow.python.training.server_lib.ClusterSpec object at 0x7f35edd3fe48\u003e, '_task_type': 'worker', '_task_id': 0, '_global_id_in_cluster': 0, '_master': 'grpc://10.18.219.10:8470', '_evaluation_master': 'grpc://10.18.219.10:8470', '_is_chief': True, '_num_ps_replicas': 0, '_num_worker_replicas': 1, '_tpu_config': TPUConfig(iterations_per_loop=234, num_shards=None, num_cores_per_replica=None, per_host_input_for_training=2, tpu_job_name=None, initial_infeed_sleep_secs=None, input_partition_dims=None), '_cluster': \u003ctensorflow.python.distribute.cluster_resolver.tpu_cluster_resolver.TPUClusterResolver object at 0x7f35fe32c8d0\u003e}\n",
            "INFO:tensorflow:_TPUContext: eval_on_tpu True\n",
            "INFO:tensorflow:Querying Tensorflow master (grpc://10.18.219.10:8470) for TPU system metadata.\n",
            "INFO:tensorflow:Found TPU system:\n",
            "INFO:tensorflow:*** Num TPU Cores: 8\n",
            "INFO:tensorflow:*** Num TPU Workers: 1\n",
            "INFO:tensorflow:*** Num TPU Cores Per Worker: 8\n",
            "INFO:tensorflow:*** Available Device: _DeviceAttributes(/job:worker/replica:0/task:0/device:CPU:0, CPU, -1, 5500052682987470911)\n",
            "INFO:tensorflow:*** Available Device: _DeviceAttributes(/job:worker/replica:0/task:0/device:XLA_CPU:0, XLA_CPU, 17179869184, 6028402093884317175)\n",
            "INFO:tensorflow:*** Available Device: _DeviceAttributes(/job:worker/replica:0/task:0/device:TPU:0, TPU, 17179869184, 1015491410753059348)\n",
            "INFO:tensorflow:*** Available Device: _DeviceAttributes(/job:worker/replica:0/task:0/device:TPU:1, TPU, 17179869184, 9892516086734793051)\n",
            "INFO:tensorflow:*** Available Device: _DeviceAttributes(/job:worker/replica:0/task:0/device:TPU:2, TPU, 17179869184, 6204465791995677744)\n",
            "INFO:tensorflow:*** Available Device: _DeviceAttributes(/job:worker/replica:0/task:0/device:TPU:3, TPU, 17179869184, 3155068735017297531)\n",
            "INFO:tensorflow:*** Available Device: _DeviceAttributes(/job:worker/replica:0/task:0/device:TPU:4, TPU, 17179869184, 14411619360662689937)\n",
            "INFO:tensorflow:*** Available Device: _DeviceAttributes(/job:worker/replica:0/task:0/device:TPU:5, TPU, 17179869184, 11467280455001446031)\n",
            "INFO:tensorflow:*** Available Device: _DeviceAttributes(/job:worker/replica:0/task:0/device:TPU:6, TPU, 17179869184, 5770875602062311761)\n",
            "INFO:tensorflow:*** Available Device: _DeviceAttributes(/job:worker/replica:0/task:0/device:TPU:7, TPU, 17179869184, 1289596734364493101)\n",
            "INFO:tensorflow:*** Available Device: _DeviceAttributes(/job:worker/replica:0/task:0/device:TPU_SYSTEM:0, TPU_SYSTEM, 17179869184, 4967910847423677762)\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/python/ops/resource_variable_ops.py:435: colocate_with (from tensorflow.python.framework.ops) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Colocations handled automatically by placer.\n",
            "INFO:tensorflow:Calling model_fn.\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/python/keras/layers/core.py:143: calling dropout (from tensorflow.python.ops.nn_ops) with keep_prob is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Please use `rate` instead of `keep_prob`. Rate should be set to `rate = 1 - keep_prob`.\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/python/ops/losses/losses_impl.py:209: to_float (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Use tf.cast instead.\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/python/ops/math_ops.py:3066: to_int32 (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Use tf.cast instead.\n",
            "INFO:tensorflow:Create CheckpointSaverHook.\n",
            "INFO:tensorflow:Done calling model_fn.\n",
            "INFO:tensorflow:TPU job name worker\n",
            "INFO:tensorflow:Graph was finalized.\n",
            "INFO:tensorflow:Running local_init_op.\n",
            "INFO:tensorflow:Done running local_init_op.\n",
            "INFO:tensorflow:Saving checkpoints for 0 into gs://gm-bucket/mnistjobs/job-2019-03-15-19:21:55/model.ckpt.\n",
            "INFO:tensorflow:Initialized dataset iterators in 0 seconds\n",
            "INFO:tensorflow:Installing graceful shutdown hook.\n",
            "INFO:tensorflow:Creating heartbeat manager for ['/job:worker/replica:0/task:0/device:CPU:0']\n",
            "INFO:tensorflow:Configuring worker heartbeat: shutdown_mode: WAIT_FOR_COORDINATOR\n",
            "\n",
            "INFO:tensorflow:Init TPU system\n",
            "INFO:tensorflow:Initialized TPU in 7 seconds\n",
            "INFO:tensorflow:Starting infeed thread controller.\n",
            "INFO:tensorflow:Starting outfeed thread controller.\n",
            "INFO:tensorflow:Enqueue next (234) batch(es) of data to infeed.\n",
            "INFO:tensorflow:Dequeue next (234) batch(es) of data from outfeed.\n",
            "INFO:tensorflow:loss = 0.13176687, step = 234\n",
            "INFO:tensorflow:Enqueue next (234) batch(es) of data to infeed.\n",
            "INFO:tensorflow:Dequeue next (234) batch(es) of data from outfeed.\n",
            "INFO:tensorflow:loss = 0.12924866, step = 468 (0.539 sec)\n",
            "INFO:tensorflow:global_step/sec: 434.272\n",
            "INFO:tensorflow:examples/sec: 111174\n",
            "INFO:tensorflow:Enqueue next (234) batch(es) of data to infeed.\n",
            "INFO:tensorflow:Dequeue next (234) batch(es) of data from outfeed.\n",
            "INFO:tensorflow:loss = 0.026477287, step = 702 (0.238 sec)\n",
            "INFO:tensorflow:global_step/sec: 981.384\n",
            "INFO:tensorflow:examples/sec: 251234\n",
            "INFO:tensorflow:Enqueue next (234) batch(es) of data to infeed.\n",
            "INFO:tensorflow:Dequeue next (234) batch(es) of data from outfeed.\n",
            "INFO:tensorflow:loss = 0.0033653756, step = 936 (0.239 sec)\n",
            "INFO:tensorflow:global_step/sec: 981.105\n",
            "INFO:tensorflow:examples/sec: 251163\n",
            "INFO:tensorflow:Enqueue next (234) batch(es) of data to infeed.\n",
            "INFO:tensorflow:Dequeue next (234) batch(es) of data from outfeed.\n",
            "INFO:tensorflow:loss = 0.022911828, step = 1170 (0.238 sec)\n",
            "INFO:tensorflow:global_step/sec: 982.213\n",
            "INFO:tensorflow:examples/sec: 251446\n",
            "INFO:tensorflow:Enqueue next (234) batch(es) of data to infeed.\n",
            "INFO:tensorflow:Dequeue next (234) batch(es) of data from outfeed.\n",
            "INFO:tensorflow:loss = 0.030684669, step = 1404 (0.237 sec)\n",
            "INFO:tensorflow:global_step/sec: 987.057\n",
            "INFO:tensorflow:examples/sec: 252687\n",
            "INFO:tensorflow:Enqueue next (234) batch(es) of data to infeed.\n",
            "INFO:tensorflow:Dequeue next (234) batch(es) of data from outfeed.\n",
            "INFO:tensorflow:loss = 0.07946512, step = 1638 (0.238 sec)\n",
            "INFO:tensorflow:global_step/sec: 983.899\n",
            "INFO:tensorflow:examples/sec: 251878\n",
            "INFO:tensorflow:Enqueue next (234) batch(es) of data to infeed.\n",
            "INFO:tensorflow:Dequeue next (234) batch(es) of data from outfeed.\n",
            "INFO:tensorflow:loss = 0.0021402398, step = 1872 (0.243 sec)\n",
            "INFO:tensorflow:global_step/sec: 963.441\n",
            "INFO:tensorflow:examples/sec: 246641\n",
            "INFO:tensorflow:Enqueue next (234) batch(es) of data to infeed.\n",
            "INFO:tensorflow:Dequeue next (234) batch(es) of data from outfeed.\n",
            "INFO:tensorflow:loss = 0.017131934, step = 2106 (0.240 sec)\n",
            "INFO:tensorflow:global_step/sec: 976.482\n",
            "INFO:tensorflow:examples/sec: 249979\n",
            "INFO:tensorflow:Enqueue next (234) batch(es) of data to infeed.\n",
            "INFO:tensorflow:Dequeue next (234) batch(es) of data from outfeed.\n",
            "INFO:tensorflow:loss = 0.0011579404, step = 2340 (0.230 sec)\n",
            "INFO:tensorflow:global_step/sec: 1015.67\n",
            "INFO:tensorflow:examples/sec: 260011\n",
            "INFO:tensorflow:Saving checkpoints for 2340 into gs://gm-bucket/mnistjobs/job-2019-03-15-19:21:55/model.ckpt.\n",
            "INFO:tensorflow:Stop infeed thread controller\n",
            "INFO:tensorflow:Shutting down InfeedController thread.\n",
            "INFO:tensorflow:InfeedController received shutdown signal, stopping.\n",
            "INFO:tensorflow:Infeed thread finished, shutting down.\n",
            "INFO:tensorflow:infeed marked as finished\n",
            "INFO:tensorflow:Stop output thread controller\n",
            "INFO:tensorflow:Shutting down OutfeedController thread.\n",
            "INFO:tensorflow:OutfeedController received shutdown signal, stopping.\n",
            "INFO:tensorflow:Outfeed thread finished, shutting down.\n",
            "INFO:tensorflow:outfeed marked as finished\n",
            "INFO:tensorflow:Shutdown TPU system.\n",
            "INFO:tensorflow:Loss for final step: 0.0011579404.\n",
            "INFO:tensorflow:training_loop marked as finished\n",
            "INFO:tensorflow:Calling model_fn.\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/contrib/tpu/python/tpu/tpu_estimator.py:2655: div (from tensorflow.python.ops.math_ops) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Deprecated in favor of operator or tf.math.divide.\n",
            "INFO:tensorflow:Done calling model_fn.\n",
            "INFO:tensorflow:Starting evaluation at 2019-03-15T19:22:23Z\n",
            "INFO:tensorflow:TPU job name worker\n",
            "INFO:tensorflow:Graph was finalized.\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/python/training/saver.py:1266: checkpoint_exists (from tensorflow.python.training.checkpoint_management) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "Use standard file APIs to check for files with this prefix.\n",
            "INFO:tensorflow:Restoring parameters from gs://gm-bucket/mnistjobs/job-2019-03-15-19:21:55/model.ckpt-2340\n",
            "INFO:tensorflow:Running local_init_op.\n",
            "INFO:tensorflow:Done running local_init_op.\n",
            "INFO:tensorflow:Init TPU system\n",
            "INFO:tensorflow:Initialized TPU in 8 seconds\n",
            "INFO:tensorflow:Starting infeed thread controller.\n",
            "INFO:tensorflow:Starting outfeed thread controller.\n",
            "INFO:tensorflow:Initialized dataset iterators in 0 seconds\n",
            "INFO:tensorflow:Enqueue next (1) batch(es) of data to infeed.\n",
            "INFO:tensorflow:Dequeue next (1) batch(es) of data from outfeed.\n",
            "INFO:tensorflow:Evaluation [1/1]\n",
            "INFO:tensorflow:Stop infeed thread controller\n",
            "INFO:tensorflow:Shutting down InfeedController thread.\n",
            "INFO:tensorflow:InfeedController received shutdown signal, stopping.\n",
            "INFO:tensorflow:Infeed thread finished, shutting down.\n",
            "INFO:tensorflow:infeed marked as finished\n",
            "INFO:tensorflow:Stop output thread controller\n",
            "INFO:tensorflow:Shutting down OutfeedController thread.\n",
            "INFO:tensorflow:OutfeedController received shutdown signal, stopping.\n",
            "INFO:tensorflow:Outfeed thread finished, shutting down.\n",
            "INFO:tensorflow:outfeed marked as finished\n",
            "INFO:tensorflow:Shutdown TPU system.\n",
            "INFO:tensorflow:Finished evaluation at 2019-03-15-19:22:34\n",
            "INFO:tensorflow:Saving dict for global step 2340: accuracy = 0.9931, global_step = 2340, loss = 0.027747009\n",
            "INFO:tensorflow:Saving 'checkpoint_path' summary for global step 2340: gs://gm-bucket/mnistjobs/job-2019-03-15-19:21:55/model.ckpt-2340\n",
            "INFO:tensorflow:evaluation_loop marked as finished\n",
            "INFO:tensorflow:Calling model_fn.\n",
            "INFO:tensorflow:Running infer on CPU\n",
            "INFO:tensorflow:Done calling model_fn.\n",
            "WARNING:tensorflow:From /usr/local/lib/python3.6/dist-packages/tensorflow/python/saved_model/signature_def_utils_impl.py:205: build_tensor_info (from tensorflow.python.saved_model.utils_impl) is deprecated and will be removed in a future version.\n",
            "Instructions for updating:\n",
            "This function will only be available through the v1 compatibility library as tf.compat.v1.saved_model.utils.build_tensor_info or tf.compat.v1.saved_model.build_tensor_info.\n",
            "INFO:tensorflow:Signatures INCLUDED in export for Classify: None\n",
            "INFO:tensorflow:Signatures INCLUDED in export for Regress: None\n",
            "INFO:tensorflow:Signatures INCLUDED in export for Predict: ['serving_default']\n",
            "INFO:tensorflow:Signatures INCLUDED in export for Train: None\n",
            "INFO:tensorflow:Signatures INCLUDED in export for Eval: None\n",
            "INFO:tensorflow:Restoring parameters from gs://gm-bucket/mnistjobs/job-2019-03-15-19:21:55/model.ckpt-2340\n",
            "INFO:tensorflow:Assets added to graph.\n",
            "INFO:tensorflow:No assets to write.\n",
            "INFO:tensorflow:SavedModel written to: gs://gm-bucket/mnistjobs/job-2019-03-15-19:21:55/mnist/temp-b'1552677756'/saved_model.pb\n"
          ]
        }
      ],
      "source": [
        "EPOCHS = 10\n",
        "\n",
        "# TPU_REFACTORING: to use all 8 cores, increase the batch size by 8\n",
        "GLOBAL_BATCH_SIZE = BATCH_SIZE * 8\n",
        "\n",
        "# TPU_REFACTORING: TPUEstimator increments the step once per GLOBAL_BATCH_SIZE: must adjust epoch length accordingly\n",
        "# steps_per_epoch = 60000 // BATCH_SIZE  # 60,000 images in training dataset\n",
        "steps_per_epoch = 60000 // GLOBAL_BATCH_SIZE  # 60,000 images in training dataset\n",
        "\n",
        "MODEL_EXPORT_NAME = \"mnist\"  # name for exporting saved model\n",
        "\n",
        "# TPU_REFACTORING: the TPU will run multiple steps of training before reporting back\n",
        "TPU_ITERATIONS_PER_LOOP = steps_per_epoch # report back after each epoch\n",
        "\n",
        "tf_logging.set_verbosity(tf_logging.INFO)\n",
        "now = datetime.datetime.now()\n",
        "MODEL_DIR = BUCKET+\"/mnistjobs/job\" + \"-{}-{:02d}-{:02d}-{:02d}:{:02d}:{:02d}\".format(now.year, now.month, now.day, now.hour, now.minute, now.second)\n",
        "\n",
        "# TPU REFACTORING: the RunConfig has changed\n",
        "#training_config = tf.estimator.RunConfig(model_dir=MODEL_DIR, save_summary_steps=10, save_checkpoints_steps=steps_per_epoch, log_step_count_steps=steps_per_epoch/4)\n",
        "training_config = tf.contrib.tpu.RunConfig(\n",
        "    cluster=tpu,\n",
        "    model_dir=MODEL_DIR,\n",
        "    tpu_config=tf.contrib.tpu.TPUConfig(TPU_ITERATIONS_PER_LOOP))\n",
        "   \n",
        "# TPU_REFACTORING: exporters do not work yet. Must call export_savedmodel manually after training\n",
        "#export_latest = tf.estimator.LatestExporter(MODEL_EXPORT_NAME, serving_input_receiver_fn=serving_input_fn)\n",
        "    \n",
        "# TPU_REFACTORING: Estimator =\u003e TPUEstimator\n",
        "#estimator = tf.estimator.Estimator(model_fn=model_fn, config=training_config)\n",
        "estimator = tf.contrib.tpu.TPUEstimator(\n",
        "    model_fn=model_fn,\n",
        "    model_dir=MODEL_DIR,\n",
        "    # TPU_REFACTORING: training and eval batch size must be the same for now\n",
        "    train_batch_size=GLOBAL_BATCH_SIZE,\n",
        "    eval_batch_size=10000,  # 10000 digits in eval dataset\n",
        "    predict_batch_size=10000, # prediction on the entire eval dataset in the demo below\n",
        "    config=training_config,\n",
        "    use_tpu=USE_TPU,\n",
        "    # TPU REFACTORING: setting the kind of model export we want\n",
        "    export_to_tpu=False)  # we want an exported model for CPU/GPU inference because that is what is supported on ML Engine\n",
        "\n",
        "# TPU REFACTORING: train_and_evaluate does not work on TPU yet, TrainSpec not needed\n",
        "# train_spec = tf.estimator.TrainSpec(training_input_fn, max_steps=EPOCHS*steps_per_epoch)\n",
        "# TPU REFACTORING: train_and_evaluate does not work on TPU yet, EvalSpec not needed\n",
        "# eval_spec = tf.estimator.EvalSpec(validation_input_fn, steps=1, exporters=export_latest, throttle_secs=0) # no eval throttling: evaluates after each checkpoint\n",
        "\n",
        "# TPU REFACTORING: train_and_evaluate does not work on TPU yet, must train then eval manually\n",
        "# tf.estimator.train_and_evaluate(estimator, train_spec, eval_spec)\n",
        "estimator.train(training_input_fn, steps=steps_per_epoch*EPOCHS)\n",
        "estimator.evaluate(input_fn=validation_input_fn, steps=1)\n",
        "  \n",
        "# TPU REFACTORING: exporters do not work yet. Must call export_savedmodel manually after training\n",
        "estimator.export_savedmodel(os.path.join(MODEL_DIR, MODEL_EXPORT_NAME), serving_input_fn)\n",
        "tf_logging.set_verbosity(tf_logging.WARN)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "9jFVovcUUVs1"
      },
      "source": [
        "### Visualize predictions"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 574
        },
        "colab_type": "code",
        "id": "yJNQlhN2jjYm",
        "outputId": "6c3c6eed-4030-44a8-acd3-73d95954953d"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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W7OxsxMXFce1L27dvL5hWZejr68PR0RFAWTv6usLS0pL73KBBA8F0du/ejZ9/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\nTkSuQmCC\n",
            "text/plain": [
              "\u003cFigure size 936x216 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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AzaguK0NZRiae/rgDJoMHgt/GqMFnfrF3HyKmzWQ7IqWpaSjPzGxxqENjsZ4+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\n",
            "text/plain": [
              "\u003cFigure size 936x216 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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t2hCARq1MzKfc1McYJ6peiftFI//am6urK8XHx0s6s/f9998LmXKA6pR7Yg8a\n1TTG+WdheXm5kC3JyclJkrU/GqKqqooiIiLIy8tL70FdPkvPywZWFxYWklwu/1Ma46YQiX//+9/Y\nt28ffv31V9y7d6/BYzMyMpCcnIzg4GCx5F8phg8fjnbt2mHgwIE4fPgwli9fjsDAQNF1tmzZgoUL\nF9baz3EcWrRogTVr1qBZs2YAgIkTJ6KsrAylpaV6adra2mLcuHH43//9XygUCqxbtw43btwAACiV\nSr3Krsnf//53WFtbg4hQUVEh7D937pzwu7e3t6ia//73v5GRkQEACA0NRUJCAhwcHHSOKSsrQ3x8\nPABg0aJFiIyMFLUOL4OtrS0AoLi4WDKNhw8fAgDMzMwk0zA0Tk5OqKysfOFxaWlpyMnJAQDMmzcP\n7du3F0XfwcEBU6dOBQBcu3YNS5cuxZkzZ/DRRx+hdevWmD59OgDA2tpaFD2ebdu2Aahur425T7/6\n6iucO3cOmzdvbnKd7O3tAQB79uwBALi5uWHSpEmIiorSOe7y5csAAE9Pzybp1GT48OFwdHTEnTt3\ndPZHR0fj1q1bwt+RkZF48803RdGsya1bt/Cvf/0LABAREYHRo0dLotMYFAoFFAoFACA7OxstWrTA\n7du3m1yeiYkJxowZg+7duyMkJOSl/qesrAxffvklPDw8EBcX12RtABg0aBB69+6NRYsWCWVVVVXV\ne/zNmzcREREBV1dXDBo0SC/tutixYwfi4uKQmZkJAOjevTt+/vlnoc8WCxcXF9y8eVP4u1evXgCA\nXbt24fz581i+fDkA8Z/LL4LjOMTFxaFTp044fvw4hg4d2uSyEhMT4enpKfSLDVFSUoLo6GhUVlai\nbdu2TdY0GvqOjBcXF9N7770nTDvWtfG+kABo5MiRtHv37ka/TeiLIUfGea5evUoODg7k4eEh+gj5\noUOHhBHwmluvXr1q5SJ3dnamM2fOiKKtVqtpxIgRZGtrS25ubrRv3z5q1aqV6G4qRNXpBWtm49GO\n1hdztGHNmjVCVphx48bVuSIjEVF8fDwB1SusiT2tnZmZSZmZmS/M+qNWq4njOPL29hZVXxt+xmP0\n6NGSaTSE2CPjOTk5dODAgRced/nyZYqNjaUuXbrovVjWiygpKaEBAwYQUL34kVTwmStOnjz50v8z\nYcIEUigUFBERoXeO6nXr1lFISAjNnTu33nu2rvRsYsLnGddeEMjc3FySUTS+7fIZmaZOnSp5jMW6\ndevIz89PJ9d3TU6ePElHjx4V+mpbW1udUXE3NzdJ68jDuwJOnjxZ1HL5LFYnTpyg8PBwHd9ufhs9\nejSFh4eLksdfm6ysLIqOjhajTgEjAAATXElEQVSeIQqFgkaOHCn6iDjPwYMHBRdCV1dXmj9/Pl24\ncIFsbGyoe/fu9PDhQ4O4ytZHRESE3ovTDRgwgLy9vV/oSZGenk6urq4EgD799FO9NF+GV9JNpaio\niKZMmUIKhYK6detGsbGxQi7bwMBAOnXqFD158oROnTpFp06dEm2548ZiDGOcqHq6ysnJifr37y9q\nuTNnziQ7O7taHY2HhwfFxcVRdHS0kGP4+vXrtHDhQlH1iaoXdeBX9FOpVJIY43UBQEiJJlZ+8dOn\nTwu+h0qlssFOLDQ0lACIvtBQQUGBsErgi3Lv8sa4m5sbPXr0SNT0aDx8kMpfxRh/Gfbv3082NjZk\nZ2dHYWFh9b6QicXGjRvJ3NycAgICJEuFSfRfN5UX5S8vLy+nadOm0bRp08jCwoKGDBlC+fn5ktVL\nm1mzZhEgXmrUmqxYsYJWrFghGJ7Ozs56rb9QH5WVlTRz5kxhwbCQkBC6deuW6Do8vNHF52pXKpW0\nceNGOnv2LJ09e5YWLlxI77zzDvXu3Zvkcnm97jpWVlaS1lObXr16kaOjo+TrFPTu3bvWM7KpLmeb\nN28mf3//WrEjly5dIn9/f2rXrp2g0bVrV9qwYYMIZ1A/p06dInNzc3J2dhYSC7i7u5ONjY3o/ulN\nYcCAAaIY40B1EoXNmzeTWq2m8vJyKi8vpxMnTtDq1aspICBASObwzTffSBL3URP+2dizZ89GL+hk\n0ADOjRs3ko2NDXl7exvkwrwI3meR4zi9sqncunWrSZ0Vv3RrfHx8k7XrqoupqSnJZDIhev377783\nWGdaE5VKJURvS40UxviHH35IQPUiKC8KVuSDkMVe0S49PZ2USiUplUqaMGEC7dixo96gOd4Y5ziO\njhw5ItqiIdq8jsa4j48PmZmZkbOzs+T+vaWlpYKxEB0dLakWH8Apk8nIx8eHtm/fTnl5ecLnN27c\noMjISJ0sQdOmTdOJ1ZAaqUfGaxrjYmcj4tFoNDrGn9TLoiclJVFSUlKDhjb//KsraNPDw4MCAgIM\nFqQ9depUAiBa3v6G4LMWaW9Hjx5tUllfffWVMPM8cOBAYdM2wm1tbWnYsGEGG5HmM2tpv2AePHjQ\nINoNwS8CtWPHDr3KWbVqlc53Z2pqKmzabZsfiJRipdO6+PLLLwX9r7/+ulH/K7nPuDZt27aFj48P\nbG1tYWoqicRLc/r0acycORMcx6FXr14IDw9vcllJSUn48ssv0aZNmwaPCwkJgbu7OwCgoKAABQUF\n4DgO169fb7J2Tdq1a4ekpCTcv38fkydPFq1cfThz5ozBtJydnQEAN27cEMVvvEOHDjA1NcWWLVte\n6EfYpUsXvfXqwtvbW/Cv27RpEzZt2gR7e/s6fQ15v2d7e3u0bNlSkvq8Srzxxht6l8H7x/L+stpc\nuXIFAJCamgpvb2+kp6frrfcitmzZghMnTiAgIADR0dGSallaWmLt2rWIjo5GamoqwsLC4OTkJLSt\nvLw8PH/+HC1btsTq1asBAJMmTYKJiYmk9TIkX375pfC7k5OT4FMrJSEhIZL7iQ8bNgwA4O/vj2vX\nrgmxHnVhaWkJOzs7IW7By8sL//jHPyStH49arcYHH3yAHTt2ICAgAMuWLZNcs65ndWJiInr37t3o\nshQKBaytrXH8+HGd/RzHwcHBAYsXL4abmxt69uzZ1Oo2mkmTJqFr165YunQpfvzxR/Tt2xc9evQw\nmH5dVFVVYenSpejUqRNGjBihV1mDBg3C9u3bkZycDAA6sWM8gYGBGDx4MGbMmGGw+KasrCzh9zVr\n1mDGjBn6FypVasPQ0FCKiYmRfJq3JjExMbRz507auXMnffrppySXy0kmk5FKpdL7LY0nMTGREhMT\nacyYMeTj40M+Pj7CyENDP/lVHP+KqFQqwcVCaqD1pvyipbz/bGg0GtJoNHTs2DGaPXt2g1kglEql\naHEAdfEqjYyvX79e7/Lmzp1L2dnZwjRzTk4OpaamUnx8vJAqU6lUSp7/mV+tju83tm/fLqmeNllZ\nWXTw4EEh+4WVlRW9//779Omnnxok73VDHDhwQNKRcXd3dyGby9SpUyXT0R4Zd3Z2pp07d9Ldu3cl\n09Pm9u3b1K1bN7K1tSVbW1saO3YsrVq1StiOHTtmkHpoc+fOHbpz5w716tVLGFk21MhxQUGBTswa\nABoxYkSTy7t06RI5OjoSUJ1pq3nz5pKsONlYNBoNzZkzh1xcXETN8f2yFBQUUEFBAW3YsIE6d+5M\n9vb2omVFevLkCR06dIhmz55N77//Pg0ZMoSGDBlC1tbWtGzZMknd++pj06ZNwkxUY70B2AqcDAaD\nwWAwGAzGKwZXVFRE9X0odioeqbl8+TK8vLzAcZzOfj8/P8yZM0eYzpOCH374AZ06dcK6det09l+7\ndg0eHh6wt7fHpEmT/pwpd14CFxcXdOvWDQCwe/duyXQ0Gg3kcrnwd2FhIezs7CTTe5354IMPsGHD\nBvTt2xdHjhwxuP6+ffsAAEOHDsW9e/dEccfZv38/pkyZAgcHB3Ach6qqKly5cgWdO3cGAERFRWH8\n+PF66zTE559/DgBYsGABPvroI6xYsQIyGRsXycvLQ2BgoJAqVWz69esHoDo16unTpwVXQrEhIqxd\nuxYA8MUXX+Du3bvo0qULjhw58lq4lGlz6dIl9O3bFwCQn5+PcePGYdWqVbCxsTFYHdRqNf7xj3/g\n119/BQBs2LABEyZMMJj+X5GcnBwkJyfj4MGDuHLlipAOWKlUYsWKFRg5cqTOc/qviIeHB54/f46f\nfvqpUalvnzx5Uud+4zp0i4ynpye++eYb4SHeqlUrtG/fHpGRkbCwsJBUe8yYMQAg+FsypCEpKQkA\n0Lp1awCAubm5MavzWvDjjz/i6NGj6NOnj0F1U1NThd/FeuEqKipCXl4eHjx4ACcnJ3Tq1AmXLl2C\nSqUCAFhZWYmiUx/Z2dlCGx4wYAA+++wzZoj/B2dnZ8kMcQCCb7SDg4NkhjhQ7UM8ZcoUABB+vq50\n7doVeXl5Rq2DtbW14HPMEAcXFxe4uLhg3Lhxxq6K0bh27Zqo5f2ljHEACA8P1ytIk/Fq8/bbbyMw\nMBCxsbEAqgOSGNLw+eef4/r16/D19RVGjg1JQUEBAGDOnDmivXSNHTsWY8eOFaWsptC+fXtcvHjR\naPoMGCxgkcFgMF6Wv5SbCoPBYDAYDAaD8SrSJDeV+v6JwWAwGAwGg8Fg6A9zVmQwGAwGg8FgMIwE\nM8YZDAaDwWAwGAwjwYxxBoPBYDAYDAbDSDBjnMFgMBgMBoPBMBLMGGcwGAwGg8FgMIwEM8YZDAaD\nwWAwGAwjwYxxBoPBYDAYDAbDSEhijHP37kExYQKs3dxg7eKCZiNHQnbzphRSOtgqlbBxcICNk5Ow\nWfbrJ7muSXo6LAcPhk3btrB+8000CwuDLCtLWs2UFJ3z5DdbpRImv/76l9WWXb6MZsOHw9rFBdYu\nLpBHRQEajaSaPObffAPrLl1g06IFLIODYXL2rOSaxmhbgPGus7Ha1uvYprn799Hsn/+EtasrrDt2\nhGLKFECtllxXG/OEhOprbKDlyo11rWVZWWgWFlat2749mr37LmRXr0qu+zo9E3mM1ncZ6ZyNdR8b\nq20Zs9+SZWbCKjAQNq1aiV+26CUCsBw1CgCgPn8e6vR0wNwczd5/XwqpWpTs3o3i/HxhKzlyRFrB\noiJYDh2KiqAgFN+4AXVaGqhZMzQbM0ZS2coePXTOszg/H6XffYdKlQqVPj5/Te2iIli++y6q2reH\n+uJFPP31V5hkZEC+YIF0mv/BbPNmWHzzDUp++AHFv/+O8pAQyBctAqqqpBM1Utsy5nU2Vtt6Hdt0\ns/HjQc2a4en583h64gRkd+9CERkpuS4Pd/s2LBISDKZntGtNhGZhYahq2RLqjAyor1xBVZs2sAwL\nA6jeBbBF43V5JgraxviOjXjOxryPDd62YLzzNUtKguWwYah8801JyhffGH/yBJWenni+cCGgVAJK\nJTSTJ8PkyhWgqEh0OWPDaTR49sUX0ERGAhYWgFKJ8rAwmGRlAc+fG64iJSVQREXh+ZIlgFxuOF0D\napueOweuoKC6bdnYgFq1wvPYWJj/8ANQXi6ZLgBYxMfj+ezZqPL2Bpo1Q9mMGSjZuxeQSefpZay2\nZczrXAtjteu/eJuWXboE0/Pn8Tw2FmRnB3J2xvPoaJjt3g2usFAyXW0UH38MzZQpBtECjHetuUeP\nYHLrFsrDwoBmzYBmzVA+ciRkd++Ce/xYMl1jYcxnotG+YyOd86twHxsSo56vWo2nR46gok8fSYoX\n35KwtcWzhARQmzb/Fbl9G2RjA1hbiy5XE4s1a2DVrRtsWrdGs5Ejwd2+LakeOTmhfNw4wSjjcnNh\nvm4dyocMMajxYLFyJSo7dkRF374G0zS4NtF/N36XnR244mLIcnIkk+Xu34dJTg5QVVU9RdW2LSyH\nDJF8CtJobctI17kujNWu/+pt2iQ9HVWOjqAWLYR9ld7e4CorYXLxomS6PGY7d0J2/z7Kpk2TXEvA\nSNea7O1R4ecH882bqwekSkthvmULKgICQM2bS6bL81o9E431HRvpnI19Hxu6bRnzfMvHjQO1aydZ\n+ZIHcHJ37kD++ed4HhUFmJhIqlXh44MKPz88TU6G+tw5oLKyeiqwokJSXaB6ytXGwQE2Xl6AjQ1K\nv/lGck2BoiJYrF4NzaefGk7TCNoV/v6g5s0hj4kB1Gpwf/wBi6++Aslkkr4Vy+7fBwCYb92K0s2b\nob5wAVVvvIFmI0cCZWWS6fIYum0Z6zrXwljt+nVo0wUFIKVSd2ezZiALC3CPHkmmCwAoKoJ83jw8\nW7kSMDWVVksLY7br0u++g0l6OmxVKti2bAmTM2dQmpgoqSbw+j0Tjd13GfqcjXkfG6NtGbXfkhhJ\njXFZRgas+vdH+eDBKJsxQ0opAEDJsWMomzkTsLICtWyJZ8uWwSQzEyapqZJrU9u2KH74EMUXLwJE\nsBwyxCAdHgBYbNyIyk6dUOnraxA9o2krlSjdtg0mV67ApnNnWA4divKhQwGOA8zMpNP9zyiLZvp0\nVLm4gJo3x/O4OJjk5MAkLU06XV7e0G3LWNe5BsZq169Fm+a4uv2VDeDDrJg3D+VDhqDyb3+TXEsH\nY13r8nJYhoWhIjAQxdnZKM7ORkWvXrAcPhx49kw6XbyGz0Qj910GP2cj3sdGaVtGPF+pkWxYwuTk\nSViOHQvNzJnVflRGgNq2BZmYgMvPN5xmu3YoXbkStioVTE6fRmVgoOSaZrt3oywsTHKdV0G70scH\nJYcPC39zt2+Dq6xEVcuWkmlWOToCqJ7u5KGWLUGmppDl5aFSMmVdDNm2jHGda2Ksdv1atGl7+9oj\nhWo1uLIyob1LgUlyMkyPH4f69GnJNBrCGNfa9ORJyDIy8PzHHwGFAgDw/IsvYLN+PUyTkw3qgvU6\nPBNfhb7LUOdsrPu4LgzRtl6l8xUbSUbGTdLTYTlmDJ4tW2YwQ1x24QLks2frvCHJbt6svgldXCTT\nNd2zB1YBATq6HJ9GyQBv4lxuLkwuX0aFAVIKGV1bo4HZ1q06N6PZsWOodHHR8SETG2rVCmRjA5NL\nl4R93L174CoqUKUVGyE2RmtbRrrO2hirXb8ubbryb3+D7NEjHR9Pk7Q0kIUFKr29JdM137IF3KNH\nsPbygnX79rBu3x4AYDl6NOSffCKZLgDjtevy8lp+zCgvlzYTE17TZ6KRvmNjnbOx7mNjtS1jna8h\nEN8Yr6yEYto0PI+KQvmIEaIXXx/k5ATzrVthERcHPHsG7sEDKKKiUPHWW6jq2lUy3Up/f8ju34f8\n88+BkpJqf8iYGFS1bo1KCXV5TC5cAFlYoMrVVXIto2ubm8NiyRJYLFwIaDSQXbkCi6++giYiQlpd\nU1NoPvgAFl9/DdmlS0BxMeTz51e7MnTvLpms0dqWsa6zFsZq169Lm67q3BkVb70Fxfz54B4/Bnf/\nPuSLF6Ns1CjAxkYy3WeLFkGdmoqnycnCBgClK1fieXS0ZLoAjHatKwICQG+8UZ1er7gYePoU8ri4\n6sBOf3/JdF/LZ6KRvmNjnbOx7mNjtS1jna8hEN0YNzl3DiZXr0L+xRe1FtAwSUkRW06AWrRAyfbt\nME1JgU3HjrD290eVkxNKf/hBMk1Bd+9emJw/DxtXV1h37w6usBAlO3dWp7GSGFleXrX7hIQp9l4Z\nbY6rDoTKyICNiwssR46EZvr06ih2idFER6P83XdhOXw4bDp2BKdWo2T7dknP3Whty4jXmcdY7fp1\natOl330HVFbC2tMT1m+9hSp3dzxfvFhaUaWyeqZJawMAeuON6lS4UmKsa61UomT3bsiysmDt7Q1r\nT0/Irl5Fya5dgK2tZLKv5TPRSN+xMc/ZGPexsdoWYKR+C4CVjw9snJygmDkTXEmJYNeabd0qSvlc\nUVHRn9/zncFgMBgMBoPB+BNi+OFUBoPBYDAYDAaDAYAZ4wwGg8FgMBgMhtFgxjiDwWAwGAwGg2Ek\nmDHOYDAYDAaDwWAYCWaMMxgMBoPBYDAYRoIZ4wwGg8FgMBgMhpFgxjiDwWAwGAwGg2EkmDHOYDAY\nDAaDwWAYCWaMMxgMBoPBYDAYRuL/A17rmpZn0tO9AAAAAElFTkSuQmCC\n",
            "text/plain": [
              "\u003cFigure size 936x216 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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q7ePjA7VaLcr5qqqqWpw7vLKyEn5+fuA4DmvXrm1xGXJzc5GQkIDY2Fi9oSlS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\nrxgO4xXTAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "\u003cFigure size 936x216 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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NpTnG+M6dO/XCwMSaneBDC9avXy/K/p5HXV0dKisr8Y9//ENI/CIi7Nq1S/Tp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\nnMFgMBgMBoPBMBH/Dy8WZa9yvv4IAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "\u003cFigure size 936x216 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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FClRVVaGqqopX/dLSUnz99dfc92thYYH09HReNe7du4devXqBiGBnZ4eSkhIAwKRJk3id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\nQmCC\n",
            "text/plain": [
              "\u003cFigure size 936x216 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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pqaktzkt68OCB4FHlV6KaWuKwqKgI/v7+8Pf3FxwYLi4u2LdvHx4/fozly5cL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\n",
            "text/plain": [
              "\u003cFigure size 936x216 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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hFxcX/u/x48fz5z9//rxauk4PD4+30m0sz549ox07dlB8fDwZGRkREdHs2bNp+PDhouip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\nBoPBYDAkghnjDAaDwWAwGAyGRPw/wSVnWejeDd4AAAAASUVORK5CYII=\n",
            "text/plain": [
              "\u003cFigure size 936x216 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# recognize digits from local fonts\n",
        "# TPU REFACTORING: TPUEstimator.predict requires a 'params' in ints input_fn so that it can pass params['batch_size']\n",
        "#predictions = estimator.predict(lambda:  tf.data.Dataset.from_tensor_slices(font_digits).batch(N),\n",
        "predictions = estimator.predict(lambda params:  tf.data.Dataset.from_tensor_slices(font_digits).batch(N),\n",
        "                                  yield_single_examples=False)  # the returned value is a generator that will yield one batch of predictions per next() call\n",
        "predicted_font_classes = next(predictions)['classes']\n",
        "display_digits(font_digits, predicted_font_classes, font_labels, \"predictions from local fonts (bad predictions in red)\", N)\n",
        "\n",
        "# recognize validation digits\n",
        "predictions = estimator.predict(validation_input_fn,\n",
        "                                yield_single_examples=False)  # the returned value is a generator that will yield one batch of predictions per next() call\n",
        "predicted_labels = next(predictions)['classes']\n",
        "display_top_unrecognized(validation_digits, predicted_labels, validation_labels, N, 7)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "5tzVi39ShrEL"
      },
      "source": [
        "## Deploy the trained model to ML Engine\n",
        "\n",
        "Push your trained model to production on ML Engine for a serverless, autoscaled, REST API experience.\n",
        "\n",
        "You will need a GCS bucket and a GCP project for this.\n",
        "Models deployed on ML Engine autoscale to zero if not used. There will be no ML Engine charges after you are done testing.\n",
        "Google Cloud Storage incurs charges. Empty the bucket after deployment if you want to avoid these. Once the model is deployed, the bucket is not useful anymore."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "3Y3ztMY_toCP"
      },
      "source": [
        "### Configuration"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "cellView": "both",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "colab_type": "code",
        "id": "iAZAn7yIhqAS",
        "outputId": "86bd5098-1022-4ff6-cc04-9f0a4832f1e3"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Saved model directory found:  gs://stagingtemp/mnistjobs/job-2018-11-30-03:15:01/mnist/1543547747/\n"
          ]
        }
      ],
      "source": [
        "PROJECT = \"\" #@param {type:\"string\"}\n",
        "NEW_MODEL = True #@param {type:\"boolean\"}\n",
        "MODEL_NAME = \"estimator_mnist_tpu\" #@param {type:\"string\"}\n",
        "MODEL_VERSION = \"v0\" #@param {type:\"string\"}\n",
        "\n",
        "assert PROJECT, 'For this part, you need a GCP project. Head to http://console.cloud.google.com/ and create one.'\n",
        "\n",
        "#TPU REFACTORING: TPUEstimator does not create the 'export' subfolder\n",
        "#export_path = os.path.join(MODEL_DIR, 'export', MODEL_EXPORT_NAME)\n",
        "export_path = os.path.join(MODEL_DIR, MODEL_EXPORT_NAME)\n",
        "last_export = sorted(tf.gfile.ListDirectory(export_path))[-1]\n",
        "export_path = os.path.join(export_path, last_export)\n",
        "print('Saved model directory found: ', export_path)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "zy3T3zk0u2J0"
      },
      "source": [
        "### Deploy the model\n",
        "This uses the command-line interface. You can do the same thing through the ML Engine UI at https://console.cloud.google.com/mlengine/models.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "nGv3ITiGLPL3"
      },
      "outputs": [],
      "source": [
        "# Create the model\n",
        "if NEW_MODEL:\n",
        "  !gcloud ml-engine models create {MODEL_NAME} --project={PROJECT} --regions=us-central1"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "o3QtUowtOAL-"
      },
      "outputs": [],
      "source": [
        "# Create a version of this model (you can add --async at the end of the line to make this call non blocking)\n",
        "# Additional config flags are available: https://cloud.google.com/ml-engine/reference/rest/v1/projects.models.versions\n",
        "# You can also deploy a model that is stored locally by providing a --staging-bucket=... parameter\n",
        "!echo \"Deployment takes a couple of minutes. You can watch your deployment here: https://console.cloud.google.com/mlengine/models/{MODEL_NAME}\"\n",
        "!gcloud ml-engine versions create {MODEL_VERSION} --model={MODEL_NAME} --origin={export_path} --project={PROJECT} --runtime-version=1.10"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "jE-k1Zn6kU2Z"
      },
      "source": [
        "### Test the deployed model\n",
        "Your model is now available as a REST API. Let us try to call it. The cells below use the \"gcloud ml-engine\"\n",
        "command line tool but any tool that can send a JSON payload to a REST endpoint will work."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {},
        "colab_type": "code",
        "id": "zZCt0Ke2QDer"
      },
      "outputs": [],
      "source": [
        "# prepare digits to send to online prediction endpoint\n",
        "digits = np.concatenate((font_digits, validation_digits[:100-N]))\n",
        "labels = np.concatenate((font_labels, validation_labels[:100-N]))\n",
        "with open(\"digits.json\", \"w\") as f:\n",
        "  for digit in digits:\n",
        "    # the format for ML Engine online predictions is: one JSON object per line\n",
        "    data = json.dumps({\"serving_input\": digit.tolist()})  # \"serving_input\" because that is what you defined in your serving_input_fn: {\"serving_input\": tf.placeholder(tf.float32, [None, 28, 28])}\n",
        "    f.write(data+'\\n')"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 0,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 301
        },
        "colab_type": "code",
        "id": "n6PqhQ8RQ8bp",
        "outputId": "cce754dd-c46a-42d1-8baa-4eb2ec30a846"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "\u003cFigure size 936x216 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "\u003cFigure size 936x216 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "\u003cFigure size 936x216 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        },
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "\u003cFigure size 936x216 with 1 Axes\u003e"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Request online predictions from deployed model (REST API) using the \"gcloud ml-engine\" command line.\n",
        "predictions = !gcloud ml-engine predict --model={MODEL_NAME} --json-instances digits.json --project={PROJECT} --version {MODEL_VERSION}\n",
        "\n",
        "predictions = np.array([int(p.split('[')[0]) for p in predictions[1:]]) # first line is the name of the input layer: drop it, parse the rest\n",
        "display_top_unrecognized(digits, predictions, labels, N, 100//N)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "2a5cGsSTEBQD"
      },
      "source": [
        "## What's next\n",
        "\n",
        "* Learn about [Cloud TPUs](https://cloud.google.com/tpu/docs) that Google designed and optimized specifically to speed up and scale up ML workloads for training and inference and to enable ML engineers and researchers to iterate more quickly.\n",
        "* Explore the range of [Cloud TPU tutorials and Colabs](https://cloud.google.com/tpu/docs/tutorials) to find other examples that can be used when implementing your ML project.\n",
        "\n",
        "On Google Cloud Platform, in addition to GPUs and TPUs available on pre-configured [deep learning VMs](https://cloud.google.com/deep-learning-vm/),  you will find [AutoML](https://cloud.google.com/automl/)*(beta)* for training custom models without writing code and [Cloud ML Engine](https://cloud.google.com/ml-engine/docs/) which will allows you to run parallel trainings and hyperparameter tuning of your custom models on powerful distributed hardware.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "XXSk0bENYB7-"
      },
      "source": [
        "## License"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "hleIN5-pcr0N"
      },
      "source": [
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "author: Martin Gorner\u003cbr\u003e\n",
        "twitter: @martin_gorner\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "Copyright 2018 Google LLC\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");\n",
        "you may not use this file except in compliance with the License.\n",
        "You may obtain a copy of the License at\n",
        "\n",
        "    http://www.apache.org/licenses/LICENSE-2.0\n",
        "\n",
        "Unless required by applicable law or agreed to in writing, software\n",
        "distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "See the License for the specific language governing permissions and\n",
        "limitations under the License.\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "This is not an official Google product but sample code provided for an educational purpose\n"
      ]
    }
  ],
  "metadata": {
    "accelerator": "GPU",
    "colab": {
      "collapsed_sections": [
        "N6ZDpd9XzFeN"
      ],
      "name": "MNIST Estimator to tpuestimator.ipynb",
      "provenance": [],
      "toc_visible": true,
      "version": "0.3.2"
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}
